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# Exact learning augmented naive Bayes classifier

*Proceedings of the Ninth International Conference on Probabilistic Graphical Models*, PMLR 72:439-450, 2018.

#### Abstract

For classification problems, Bayesian networks are often used to infer a class variable when given feature variables. Earlier reports have described that classification accuracies of Bayesian networks achieved by maximizing the marginal likelihood (ML) were lower than those achieved by maximizing the conditional log likelihood (CLL) of a class variable given the feature variables. However, the reports stated no reason why CLL outperformed ML. Differences between the two scores’ performances in those earlier studies might depend on their respective learning algorithms: they were approximate learning algorithms, not exact ones. The present study compared the classification performances of Bayesian networks with exact learning using ML and those with approximate learning using CLL. Results demonstrate that the performance of Bayesian networks achieved by maximizing ML is not necessarily worse than that achieved by maximizing CLL. However, the results also show that classification accuracies with exact learning by ML are much worse than those by other methods when the class variable has numerous parents and few children. To resolve this difficulty, this study proposed exact learning augmented naive Bayes (ANB) using Markov blanket feature selection. Some comparison experiments demonstrated that the proposed method outperforms the other methods.